Strength of Materials
Strength of materials (mechanics of materials) connects loads to internal stresses and deformations. It is the bridge between statics and real component design: given a load, will the part yield, deflect too much, or buckle?
Stress and Strain
Normal stress sigma = P/A and shear stress tau = V/A express internal force per unit area. In the elastic region, Hooke's law relates them to strain through the modulus of elasticity: sigma = E·epsilon. Axial elongation is delta = P·L/(A·E).
Beams: Shear and Moment
Transverse loads create internal shear and bending moment that vary along a beam. For a simply supported beam with a central point load, the maximum moment is P·L/4; for a uniform load it is w·L^2/8. Bending stress is sigma = M·c/I.
Combined Loading and Failure
Superposition adds stresses from axial, bending, and torsional loads. Failure criteria include yielding (Tresca, von Mises), Euler buckling of slender columns, and fatigue under cyclic loading. A factor of safety keeps working stress below the allowable value.